Convection is defined as, quote, "heat transfer by mass motion of a fluid such as air or water when the heated fluid is caused to move away from the source of heat, carrying energy with it."
For example, when you boil water, heated water at the bottom moves up, bringing heat up to the surface, while cold water goes down and gets heated too, going up. Rinse and repeat until the water starts to become a gas.
Thus: The current brings heat from Point A to Point B, where Point A creates heated water. Rinse and repeat, Point B to Point A, Point A to Point B, etc etc.